Vol. 60, No. 3, pp. 269-304 (2003)
General Existence Results for Second Order Nonconvex Sweeping Process with Unbounded Perturbations
Messaoud BounkhelDepartment of Mathematics, College of Science,
King Saud University, P.O. Box 2455, Riyadh 11451 -- SAUDI ARABIA
Abstract: This paper is devoted to study the existence of solutions for general second order sweeping processes with perturbations of the form $\dot x(t)\in K(x(t))$, $\ddot x(t)\in-N(K(x(t));\dot x(t))+F(t,x(t),\dot x(t))+G(t,x(t),\dot x(t))$, where $K$ is a nonconvex set-valued mapping with compact values, $F$ is an unbounded scalarly upper semicontinuous convex set-valued mapping, and $G$ is an unbounded continuous non convex set-valued mapping taking their values in separable Hilbert spaces.
Keywords: uniformly prox-regular set; normal cone; subdifferential; second order nonconvex sweeping processes.
Classification (MSC2000): 34A60, 34G25, 49J52.
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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.